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One algorithm that is simple, but not very efficient, is to try out different numbers. Example, cubic root of 10:

2 cubed is 8, which is less than 10

3 cubed is 27, which is greater than 10

So the cubic root of 10 would be somewhere between 2 and 3; you can continue narrowing it down that way.

A calculator or computer program such as Excel would probably solve a cubic root - or any other root for that matter - using powers. For example, the cubic root of 10 is the same as 10 to the power (1/3).

Powers, in turn, are calculated using infinite series, using the formula:

a ^ b = exp(b ln a)

In this formula, exp() is the exponential function (e to the power ...), and "^" stands for power.

An "infinite series" is not as bad as it sounds; you don't actually calculate an infinite number of terms. Rather, the terms in an infinite series get smaller and smaller, once the terms are smaller than the desired accuracy, you can stop. It's actually a bit more complicated than that, but that's the basic idea.

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Q: How do you solve cube roots using algorithms?
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